Factors of 48 - Definition, Examples, Quiz, FAQ, Trivia
Learn to find factors using different methods with visual examples and practice activities
What are Factors?
Factors are numbers that divide exactly into another number without leaving a remainder. For example, the factors of 48 are numbers that can multiply together to give 48.
Think of factors as building blocks. Just like you can build a wall with different arrangements of bricks, you can make 48 by multiplying different pairs of numbers.
Here are all the factors of 48:
Key Concept
Factors always come in pairs. For example, 6 × 8 = 48, so both 6 and 8 are factors of 48.
How to Find Factors of 48
There are two main methods to find all the factors of a number:
Division Method
Divide 48 by whole numbers starting from 1 up to 48. If there's no remainder, both the divisor and quotient are factors.
Factor Tree Method
Break down 48 into factors until you reach prime numbers.
Remember
Stop the division method when you reach a number whose square is greater than 48. After 6, the next factors would be 8 and 6, which we already have.
Prime Factors of 48
Prime factors are the prime numbers that multiply together to give the original number. A prime number has exactly two factors: 1 and itself.
To find the prime factors of 48, we break it down into prime numbers:
Prime Factorization
We can write this as 48 = 24 × 3
This means we have four 2's and one 3 multiplied together. Let's see how this works:
Step 1: 48 ÷ 2 = 24
Step 2: 24 ÷ 2 = 12
Step 3: 12 ÷ 2 = 6
Step 4: 6 ÷ 2 = 3
Step 5: 3 ÷ 3 = 1
The prime factors are all the prime numbers we divided by: 2, 2, 2, 2, and 3.
Prime Tip
Prime factorization is like taking a number apart into its smallest building blocks. Every number has a unique set of prime factors!
Factor Pairs of 48
Factor pairs are two numbers that multiply together to give the original number. For 48, we have:
| Positive Pairs | Negative Pairs |
|---|---|
| 1 × 48 | -1 × -48 |
| 2 × 24 | -2 × -24 |
| 3 × 16 | -3 × -16 |
| 4 × 12 | -4 × -12 |
| 6 × 8 | -6 × -8 |
Pair Tip
Notice how the pairs get closer together? 1 and 48 are far apart, but 6 and 8 are close. This happens with all numbers!
Properties of Factors of 48
Let's explore some interesting properties of the factors of 48:
Sum of Factors
1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 124
Composite Number
48 is a composite number because it has more than two factors (it has 10 factors).
Even Factors
All factors of 48 are even numbers except for 1 and 3.
Divisibility
48 is divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Factors of 48 Practice Quiz
Test your knowledge about factors with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about factors:
Math Trivia
Discover interesting facts about numbers and factors:
Ancient Number Theory
The concept of factors dates back to ancient Greek mathematicians like Euclid and Pythagoras, who studied number properties around 300 BCE.
Prime Importance
Prime factorization is used in computer security for encryption. Large prime numbers help protect your online information!
Perfect Numbers
A perfect number has factors (excluding itself) that add up to the number. 6 is perfect: 1+2+3=6. The next perfect number is 28.
Largest Known Prime
The largest known prime number has over 24 million digits! Finding large primes helps mathematicians understand number patterns.
